# Homework Help: Applying the chain rule using trees?

1. Apr 29, 2013

### Pizzerer

1. The problem statement, all variables and given/known data
Write out a tree (this will be a big tree) of dependencies and hence write down an expression for
∂z/∂r

2. Relevant equations
z=k(x, y)=xy2, x=(w1)(w2)+w3, y=w4;

w1=t, w2=t2, w3=2t+1, w4=sin(t);
t=r2+2s2

3. The attempt at a solution
This is the tree I drew and followed the relevant paths in order to try and write and expression but my expression is to short. I only calculate 2 terms when there is suppose to be 8:
http://www.picpaste.com/Untitled_Image-OZCiTMvb.jpg [Broken]

This is wrong however. I need 16 leaves at the base. What am I doing wrong?

Last edited by a moderator: May 6, 2017
2. Apr 29, 2013

### Staff: Mentor

I drew a diagram and got the same one you did.

As far as your partial $\partial z/\partial r$ is concerned, I get four terms to your two. Three of the four terms look like this:
$$\frac{\partial z}{\partial x} \frac{\partial x}{\partial w_i} \frac{d w_i}{dt} \frac{\partial t}{\partial r}$$

For the fourth one, the first factor is the partial of z with respect to y.

Last edited by a moderator: May 6, 2017
3. Apr 29, 2013

### SammyS

Staff Emeritus

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